Search Results for ""

There exist a variety of formulas for either producing the nth prime as a function of n or taking on only prime values. However, all such formulas require either extremely ...

A Pythagorean quadruple is a set of positive integers a, b, c, and d that satisfy a^2+b^2+c^2=d^2. (1) For positive even a and b, there exist such integers c and d; for ...

The Schur number S(k) is the largest integer n for which the interval [1,n] can be partitioned into k sum-free sets (Fredricksen and Sweet 2000). S(k) is guaranteed to exist ...

A symmetric graph is a graph that is both edge- and vertex-transitive (Holton and Sheehan 1993, p. 209). However, care must be taken with this definition since arc-transitive ...

For a given positive integer n, does there exist a weighted tree with n graph vertices whose paths have weights 1, 2, ..., (n; 2), where (n; 2) is a binomial coefficient? ...

Place a point somewhere on a line segment. Now place a second point and number it 2 so that each of the points is in a different half of the line segment. Continue, placing ...

Bézout's theorem for curves states that, in general, two algebraic curves of degrees m and n intersect in m·n points and cannot meet in more than m·n points unless they have ...

The circumsphere of given set of points, commonly the vertices of a solid, is a sphere that passes through all the points. A circumsphere does not always exist, but when it ...

A subset tau in S_n of a permutation {1,...,n} is said to contain alpha in S_k if there exist 1<=i_1<...<i_k<=n such that tau=(tau_i,...,tau_k) is order isomorphic to ...

Let p be an odd prime and F_n the cyclotomic field of p^(n+1)th roots of unity over the rational field. Now let p^(e(n)) be the power of p which divides the class number h_n ...